Climate change is reshaping food systems and consumer practices, creating new challenges for food safety. Understanding how people modify their eating habits in response to climate disruptions and sustainability challenges is critical for assessing emerging microbiological risks. We present FoodClimNER, a new named entity recognition (NER) corpus containing extracts from open-access scientific articles on food science in the context of climate change, with manual annotations made by an expert. We define annotation guidelines with expert definitions of food practice entities and climate change entities. We evaluate baselines and a custom prompting method with recent LLMs on this task in a zero-shot setting. Results indicate that expert-level entity types and the presence of nested and discontinuous mentions make this a challenging testbed, with significant room for improving zero-shot methods. We also provide a detailed analysis of the importance of different parts of our custom prompt.